A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are given:50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45Which of the following histograms is the best representation of the data

Use law of cosines to find angles A, B, and C. Angle A = X°, B = Y° and C = Z°.

What is triangle ?

A triangle is a polygon with three sides and three angles. The sum of the three angles in a triangle always equals 180 degrees. Triangles can be classified based on the length of their sides or the measure of their angles.

We can use the law of cosines to find the angles. The law of cosines states that for any triangle, the square of one side length is equal to the sum of the squares of the other two side lengths, minus twice the product of the other two side lengths multiplied by the cosine of the angle opposite the first side.

Let A, B, and C be the angles opposite the sides of length 114 meters, 70 meters, and 95 meters, respectively.

We can use the following equation to find angle A:

cos A = (70^2 + 95^2 - 114^2) / (2 * 70 * 95)

Once we have the value of cos A, we can use the inverse cosine function to find the angle A in degrees.

Similarly, we can use the same formula to find the angle B and C.

cos B = (114^2 + 95^2 - 70^2) / (2 * 114 * 95)

cos C = (114^2 + 70^2 - 95^2) / (2 * 114 * 70)

Use law of cosines to find angles A, B, and C. Angle A = X°, B = Y° and C = Z°.

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The subjects would be randomized at random to receive the new medication, fish oil, or a placebo. The effectiveness of the new variance medicine would next be evaluated by comparing the outcomes of the various therapies.

The test would be conducted using a completely randomized experiment. This means that the 300 volunteers would be randomly assigned to the three different treatments: the new drug, fish oil, or the placebo. This ensures that any differences between the groups can be attributed to the treatments, and not any other factor. The volunteers would be monitored for a period of time, and the results of the treatments would be compared to determine the effectiveness of the new drug. This could be done through measuring changes in cholesterol and blood pressure levels, as well as any side effects of the treatments. In addition, the volunteers’ health and dietary habits should be monitored to ensure that any differences between the treatments are not caused by any other factors.

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For a quadratic function [tex]y=ax^2+bx+c[/tex], we know the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].

It is easy to see that for a function of the form [tex]y=a(x-h)^2+k[/tex], the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].

Therefore, the vertex of the graph of [tex]f(x)[/tex] is a maximum, and the vertex of the graph of [tex]g(x)[/tex] is a minimum.

By using the Trapezoidal sum with the four subintervals indicated by the table the sum is 52.95.

What is Trapezoidal sum?

The trapezoidal rule is a method for roughly approximating the definite integral in calculus. The area of the region that roughly fits the shape of a trapezoid under the graph of the function f(x) is how the trapezoidal rule operates.

A Riemann sum is a technique for calculating the area under a curve by adding the areas of rectangles or trapezoids drawn along the curve. Triangular Riemann Sum: A trapezoidal Riemann sum determines the area under a curve by adding the areas of trapezoids.

Let,  [tex]\frac{1}{10}\int\limits^1_00 {H(t)} \, dt[/tex]  is the average temperature of the tea, in degree Celsius, over the 10 minutes.

[tex]\frac{1}{10}\int\limits^1_0_0 {H(t)} \, dt = \frac{1}{10}(2*\frac{66+60}{2}+ 3*\frac{60 + 52}{2}+4*\frac{52+44}{2}+1*\frac{44+43}{2} \\ \frac{1}{10}\int\limits^1_0_0 {H(t)} \, dt = 52.95[/tex]  

Hence, by using the Trapezoidal sum with the four subintervals indicated by the table the sum is 52.95.

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1800 * ? * 1 = 198

let x be the ?

By shifting 1800*1 into right hand side

x= 198/1800

x= 11/100= 0.11

Final answer = 0.11

In the triangle the line segment joining the midpoints 'S' and 'T' of the sides PQ and PR implies that ST || QR.

As given in the question,

Diagram is attached.

As per the attached diagram  we have,

Given : In triangle PQR with midpoints S and T of sides PQ and PR respectively.

To prove : ST is parallel to QR.

Proof : First construct a line through R parallel to PQ such that it meet the extended line of ST at point 'U'

In triangle PST and triangle RTU,

PQ|| RU and SU is the transversal

∠PST ≅ ∠RUT ( alternate angles )

∠PTS ≅ ∠RTU ( vertically opposite angles)

PT ≅TR ( 'T' is the midpoint of PR )

By AAS we have

ΔPST ≅ΔRTU

By congruent part of congruent triangle we have,

PS ≅ RU

⇒ SQ ≅ RU

In quadrilateral QSUR,

SQ ≅ RU

SQ || RU ( as PQ || RU by construction )

Quadrilateral with one pair of opposite side congruent and parallel implies it is a parallelogram.

Quadrilateral QSUR is a parallelogram.

⇒ SU || QR

S - T - U

⇒ ST is parallel to QR

Therefore, in the given triangle line segment formed by joining the midpoints of the other two sides is parallel to third side.

The above question is incomplete , the complete question is :

Prove theorem 8.9 : The line segment joining the midpoints of the two sides of the given triangle is parallel to the third side .

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The area of the trapezium is 36.3 unit squared.

The figure above is a trapezium. Therefore, the area of a trapezium can be represented as follows:

Hence,

area of a trapezium = 1 / 2 (a + b)h

where

Therefore,

area of a trapezium = 1 / 2 (a + b)h

where

Using Pythagoras's theorem,

c² = a² + b²

where

h² = 6² - 1.5²

h²= 36 - 2.25

h = √33.75

h = 5.80947501931

h = 5.81

Therefore,

area of the trapezium = 1 / 2 (4 + 8.5)5.8

area of the trapezium = 1 / 2 (12.5)5.8

area of the trapezium = 72.5 / 2

area of the trapezium = 36.3 units²

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If the volume of the square based Pyramid is 125 m³ and the base is of 5m then the height of the pyramid is 15 m .

The Volume of the Square based pyramid is = 125 m³ ;

the measure of the side of base of pyramid is = 5m ;

So , the Area of the base of pyramid is = [tex]5 \times 5[/tex] = 25 m² ;

We know that the formula for the Volume of the pyramid is = [tex]\frac{1}{3} \times Area\; Of \;Square \times Height[/tex] ;

Substituting the values  ;

we get ;

⇒ [tex]125= \frac{1}{3} \times 25 \times Height[/tex] ;

On solving further ,

we get ;

⇒ [tex]\frac{125\times 3}{25}[/tex]

⇒ 15 m .

Therefore , The Height of the Pyramid is 15 m.

The given question is incomplete , the complete question is

This square-based oblique pyramid has a volume of 125 m³ and the length of the side of the base is 5m . What is the height of the pyramid ?

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3% is the percentage rate of increase or decrease.

What does exponential decay mean?

A process known as exponential decay describes how a quantity depletes over time, with the rate of depletion become proportionately slower as the quantity shrinks. Finding the exponential drop—a rapid reduction over time—is made easier by the exponential decay formula.        

                                The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay. The formula for f(x) is f(x) = a (1 - r)x.

The formula for exponential decay is y=a(1-r)x.

r is the decay rate, expressed as a decimal.

In this case, r = .03 which represents 3%

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It will take the rescue craft 0.44 hours or 26.4 minutes to reach the sailboat.

The time required for the rescue craft to reach the sailboat can be calculated by using the formula for relative velocity:

Relative Velocity = Velocity of the Rescue Craft - Velocity of the Sailboat

= 29 mph - 4 mph = 25 mph

Therefore, the time required for the rescue craft to reach the sailboat is given by:

time= Distance/Relative Velocity

= 11 miles/25 mph

= 0.44 hours

Therefore, it will take the rescue craft 0.44 hours or 26.4 minutes to reach the sailboat.

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Answer: 14.825

Step-by-step explanation:

First , do 2 * 5.3 because it's 2a, you'll have to do 2 * a. This equals 10.6.

Second, you'll need to do 5.3 * 1.25. Why? Because in the problem you need to do a * b, which is that. It equals 6.62500.

Lastly, put it all together! 10.6 + 6.62500 - 2.4 equals 14.825.

Answer: 36x + 68

Step-by-step explanation:

Expanding it, you get:

36x + 72 - 4

= 36x + 68

Answer:

-----------------------------------------------

Let the cost of a 1 kg of apples be x.

Then pear costs x - 1.12 and banana costs x + 2.35.

The total cost is 25.02:

The cost of putting sod on the gard, given the area of the trapezoid backyard of the new home, is $ 864 . 40

The backyard of the new home is said to be shaped like a trapezoid which means that the cost of putting sod on the gard can be found by checking for the area of the trapezoid.

The area of a trapezoid can be found by the formula :

= (( Base A + Base B ) x height ) / 2

= ( ( 73 + 111 ) x 40 ) / 2

= 3, 680 square feet

The cost of putting sod on the gard is therefore:

= Area of the backyard x cost per square foot of sod

= 3, 680 x 0. 23

= $ 864 . 40

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Formula data type is used to determine different values based on a variety of fields in the existing table.

It also helps to create a pattern that takes input from all the fields and gives you the final value. Other fields include constants or functions and by using formula data type, you can remove the need to repeatedly enter the same information again and again. It also eliminated the margin of error that could occur during manual entry in the entirety of your work. Formula data type is used to help solve a combination of different equations that have different fields and/or equations.

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Answer:

26 - 11 = 15

Step-by-step explanation:

The measure of the middle angle of  triangle abc is 52°

Let the largest angle of triangle be x, the smallest angle be z, and the third angle be y.

Given that the measure of the largest angle is 32 less than 3 times the smallest angle.

So, we get an equation,

x = 3z - 32              ............(1)

Also, the measure of the middle angle is 8 more than half the measure of the largest angle.

So, we get an equation,

y = 8 + (x/2)          .......(2)

From equation (1),

z = (x + 32)/3           ..........(3)

We know that the sum of all angles of triangle is 180 degrees.

x + y + z = 180

Substitute the values of y and z in above equation.

x + 8 + (x/2) + (x + 32)/3 = 180

6x + 48 + 3x + 2(x + 32) = 1080

9x + 48 + 2x + 64 = 1080

11x + 112 = 1080

11x = 1080 - 112

11x = 968

x = 88

Substituting above value of x in equation (2)

y =  8 + (88/2)

y = 8 + 44

y = 52 degrees

Therefore, the middle angle of triangle measures 52 degrees.

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Answer: 42.5

Step-by-step explanation:

8 multipled by 42.5 is 340. A strategy i use is multiply 8 by 5 or 10, for example 8 times 5 is 40, so i know that 8 times 50 is 400, that tells you the answer you need is just a little below 50

In this problem, you have a square with side length 6 and four smaller squares with side length 2 placed in the corners. The points W, X, Y, and Z are the vertices of the smaller squares. The goal is to find the maximum possible distance between points A and P.

[asy] size(200); pair A,B,C,D,P,W,X,Y,Z; A=(0,4); B=(4,4); C=(4,0); D=(0,0); P=(2,2); W=(0,6); X=(6,6); Y=(6,0); Z=(0,0); draw(A--B--C--D--cycle); draw(W--X--Y--Z--cycle); draw(A--P--C); label("A",A,NW); label("B",B,NE); label("C",C,SE); label("D",D,SW); label("P",P,S); label("W",W,N); label("X",X,NE); label("Y",Y,S); label("Z",Z,SW); [/asy]

The point A is located on the bottom-left corner of the square with side length 6, and the point P is the center of the square $ABCD$. To find the maximum distance from A to P, we need to find the longest diagonal of the square $ABCD$.

The longest diagonal of a square is the one that goes from one corner of the square to the opposite corner. In this case, the longest diagonal goes from point A to point C, which is a distance of 6 units. Therefore, the maximum possible distance from A to P is 6 units.

The profit per foot of the satin ribbon that the craft store buys and sells is $0.80.

The profit generated by the craft store per foot is determined by reducing the transactions to their unit cost and price.

The profit per unit becomes the difference between the unit selling price and the unit cost.

In other words, the profit per unit is the unit rate (per-unit profit) or ratio obtained as a difference between two unit parameters.

The cost of buying 150 feet of satin ribbon = $13.50

The unit cost per foot = $0.09 ($13.50/150)

The sales price for 5 feet = $0.80

The unit selling price per foot = $0.16 ($0.80/5)

The profit per unit = $0.80 ($0.16 - $0.80)

Profit percentage = 100% ($0.80/$0.80 x 100)

Thus, we can conclude that the craft store generates a 100% profit or $0.80 per foot.

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In circle A,  angle RAS is 74 degrees and  angle RTB is 28 degrees. The measure of minor arc BR is 81 degrees.

The figure is in the attached picture.

Notice that:

AS = AR = radii of the circle.

Hence, triangle SAR is an isosceles triangle, and ∠ASR = ∠ARS.

The sum of angles in a triangle is  180°.

Therefore,

∠ARS +  ∠ASR+ 74° =  180°

Since ∠ASR = ∠ARS,

2∠ARS + 74° =  180°

2∠ARS  = 106°

∠ARS  =  53°

and

∠ASR = ∠ARS = 53°

Angle in a straight line:

∠AST  + ∠ASR =  180°

∠AST   =  180° - ∠ASR =  180° - 53°  =  127°

Refer to triangle SAT:

∠SAT  =  180° - 28° - 127°  =  25°

The measure of minor arc BR = ∠RAB

∠RAB  =  180° - 74° - 25°  

∠RAB  =  81°

The picture in your question is missing, but most likely it was in the attached picture.

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a) According to the central limit theorem, the mean is $142 and the standard deviation is $0.7488.

b) Nearly normal according to the central limit theorem.

c) 0.0901 = 9.01% probability that the average cable service paid by a sample of cable service customers exceeds $170 in the central limit theorem.

Normal probability distribution:

The normal probability distribution, discovered by Abraham De Moivre in 1733, approximates the binomial probability distribution when a particular experiment has a very large number of trials. In 1774 Laplace studied the mathematical properties of the normal probability distribution. By historical error, the discovery of the normal distribution was attributed to Gauss, first mentioned in his 1809 paper. In the 19th century, many scientists discovered that measurement errors in a particular experiment followed a pattern (usual error curve). ), which was very well approximated by this probability distribution.

Central Limit Theorem:

The central limit theorem is a statistical theory that for large sample sizes with finite variance, samples are normally distributed and the mean of the sample is approximately equal to the mean of the entire population.

According to the Question:

The average monthly charge is $142 with a standard deviation of $29.

This is μ = 142 and σ = 29

Part a:

The mean and standard deviation of the sampling distribution of x to show your research and support your argument:

1500 samples (over 30).

According to the Central Limit Theorem

The mean is 142 $

The standard deviation is s = [tex]\frac{29}{\sqrt{1500} }[/tex] = 0.7488

Part b:

Shape of sampling distribution of X.

Due to the large sample size, the shape of the sample distribution is almost normal. According to the central limit theorem, which states that the sampling distribution converges to the normal distribution as the sample size increases. Mean ~ N(142, 0.749²)

Part C:

The probability that the average cable service paid by a sample of cable service customers exceeds $170.

Therefore, by the central limit theorem, the p-value of Z when X= 170

                         Z =  x - μ/ σ

By the Central Limit Theorem:

   Z = 170 - 142 / 0.7488

      = 28/ 0.7488

      = 37.34 exceeds 0.9099

Using the Z probability calculator :

P(Z > 1.335) = 0.09093

Complete Question:

The amount people pay for cable service varies quite a bit but the mean monthly fee is $142 and the standard deviation is $29. the distribution is not normal many people pay about $76 for basic cable and about $160 for premium service but some pay much more. a sample survey is designed to ask a simple random sample of 1,500 cable service customers how much they pay. let x hat be the mean amount paid.

Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.

Part b: what is the shape of the sampling distribution of x hat justify your answer.

Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $170? show your work.

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Answer: A. Yes

B. Yes

C. No

Step-by-step explanation:

A. 2z = 40 and z = 20, 20 is a solution of the equation because when you substitute z = 20 into the equation 2z = 40, the equation becomes true.

B. n + 5 = 20 and n = 15, 15 is a solution of the equation because when you substitute n = 15 into the equation n + 5 = 20, the equation becomes true.

C. v = 12 and v = 16, 12 is not a solution of the equation because v is assigned to 12 and 16 both, but the equation only has one solution, a variable can't be assigned to two different values.

In general, when solving equations, we check if the value of the variable makes the equation true. if it does it's a solution, if not it's not a solution.

3 ice cream machines will make a total of 480 gallons for the same length of time and 4 ice cream machines will make a total of 640 gallons for the same length of time.

For the quantity 3 ice cream machines will make.

2 ice cream machines produce a total of 320 gallons in a certain amount of time.

If 2 ice cream machines can make a total of 320 gallons. Then,

3 ice cream machines will produce a total of x gallons in the same amount of time

x = (320 × 3)/2

x = 480 gallons

Hence, 3 ice cream machines will produce a total of 480 gallons.

For the quantity 4 ice cream machines will make.

If 2 ice cream machines can make a total of 320 gallons. Then,

4 ice cream machines will produce a total of y gallons in the same amount of time

y = (320 × 4)/2

y = 640 gallons

Hence, 4 ice cream machines will produce a total of 640 gallons.

--The given question is incomplete, the complete question is

"Two ice cream machines make a total of 320 gallons in a certain amount of time. Working together for the same length of time, how many gallons of ice cream can each number of machines make?

3 ice cream machines

4 ice cream machines"--

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The minimum number of hours you will have cruise control on is 1.83 hour(s) and the maximum is 2.83 hour(s).

To find the minimum and maximum numbers of hours you will have cruise control on, you need to calculate the distance you will travel with cruise control on and divide it by your speed.

The minimum distance you will travel with cruise control on is

140 miles - 30 miles = 110 miles.

The maximum distance you will travel with cruise control on is

140 miles + 30 miles = 170 miles.

To convert these distances into hours, you will divide them by your speed of 60 miles per hour.

Minimum hours: 110 miles / 60 mph = 1.83 hours

Maximum hours: 170 miles / 60 mph = 2.83 hours

Therefore, the minimum number of hours you will have cruise control on is 1.83 hour(s) and the maximum is 2.83 hour(s).

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The coefficient of x⁷ in the given expression is 16.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given is the expression [x³ + (4 / x²)]⁴.

[x³ + (4 / x²)]⁴ =  (x³ + 4x⁻²)⁴

                      = (x³ + 4x⁻²)² (x³ + 4x⁻²)²

                      = (x⁶ + 8x + 16x⁻⁴) (x⁶ + 8x + 16x⁻⁴)  

                      = x¹² + 8x⁷ + 16x² + 8x⁷ + 64x² + 128x⁻³ + 16x² + 128x⁻³ +

                         256x⁻⁸

Rearranging with like terms, we get,

                      = x¹² + 16x⁷ + 96x² + 256x⁻³ + 256x⁻⁸

Hence the coefficient of x⁷ is 16.

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The minimum monthly payment so that she avoids paying interest on the credit card is given as follows:

$150

The minimum monthly payment is obtained applying the proportions in the context of this problem.

The interest-free period is given as follows:

6 months, as long as the purchase has a value that is less than $1000.

(as stated in the problem).

The value of the TV is given as follows:

$900.

(as stated in the problem).

The minimum monthly payment is obtained with the division of the value of the TV by the length in months of the interest free period, as follows:

Minimum payment = 900/6

Minimum payment = $150.

(this is the proportion that is applied in this problem).

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Answer:

8

Step-by-step explanation:

Each of the small squares has an area of 4 square units

so its length is 2 because 2*2 =4

so 4 small squares = 8 each side

Answer:

27π

Step-by-step explanation:

Volume = 1/3πr²h
=1/3*(3)²9π
=27π